Conventionally, vehicle travel path recognition apparatuses have been proposed that detect lane markers in an input image captured in front of a vehicle by a CCD camera, and based on the results of the lane marker detection, compute road model parameters using a Kalman filter in order to represent the road shape ahead of the vehicle (see Japanese Patent Application Laid-Open (JP-A) No. 2002-109695). In the travel path recognition apparatus of JP-A No. 2002-109695, changes in the road model parameters are treated as having a probabilistic nature, and a discrete random walk model driven by fixed Gaussian white noise is defined.